The two groups have joined forces in backing a so called safeguard clause which would allow the protection of European companies operating outside Europe.
The EPP group wants multinational companies to disclose profit shifting to low tax countries.
But it says that European companies doing business outside Europe "must not be forced to reveal everything if competitors don't."
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However, this policy, supported by the ALDE group, has been condemned by the Socialists.
S&D group leader Gianni Pittella, speaking at a news conference in Parliament on Tuesday, said, "The EPP-Liberal pact will put a spoke in the wheels of attempts to tackle tax evasion. Citizens have to pay taxes and so should multinational companies.
"But the Liberals and EPP have introduced an amendment which, if not changed, would give multinationals a get out clause. This sort of thing, putting a spoke in the wheel of the planned new rules, sends a devastating message to citizens who have to pay taxes. It is scandalous."
EPP group leader Manfred Weber said, "We fully support the need for tax transparency. Our amendment is clarification and that is all. We want to fight tax evasion as much as anyone."
Dariusz Rosati, the EPP group's negotiator on new tax transparency rules for multinational companies, accused the Socialists of discriminating against European companies.
He said, "We want to make visible how multinational companies shift their profits to low tax countries. But European companies doing business outside Europe must not be forced to reveal everything if competitors don't."
Speaking ahead of a vote on the issue in Strasbourg, he said, "We will vote in favour of more far-reaching tax transparency obligations than the initial draft law. But the Socialists want to jeopardise European companies. We want a safeguard clause which allows the protection of European companies outside Europe under certain circumstances."
Parliament was due to vote in Strasbourg on the so-called public country-by-country reporting.
The safeguard clause promoted by the EPP and ALDE groups provides that companies may, under strict conditions, ask for exceptions to the disclosure of certain detailed information, but such exceptions need to be justified to and approved by the European Commission every year.
"Country-by-country reporting does not fix the problem, but makes visible where the problem lies. The next thing to do is to harmonise the way corporate tax is calculated all over Europe without levelling tax rates", Rosati said.
In the vote on country-by-country reporting Parliament will agree on its position for the forthcoming negotiations with member states.
The Commission has suggested that transnational companies are required to publish key tax data on a country-by-country basis for the EU28 as well as for countries blacklisted as tax havens.
Data for other third countries should only be reported on an aggregated level.
The Greens/EFA group say they would have favoured stricter rules.
German MEP Sven Giegold, financial and economic policy spokesperson of the Greens/EFA group, commented, "It is a shame that in the committee the conservative-liberal coalition together with the eurosceptic conservatives have introduced exemptions for corporations."
He added, "The same coalition also prevented a reduction of the high threshold for reporting companies of €750m turnover per year. In order to take effective measures against tax dumping, public country-by-country tax transparency must not be limited to a few companies. For banks and raw materials extraction companies, transparency has long been established and is universally accepted."